Note on second paragraph on second page:
"The coupling magnitude is inversely proportional to the separation distance..."
And is also reduced by the scalar dot product of the angular difference in polarization when linear polarization is used.

Remember, a modulated RF signal will have sidebands. Let's look at the simplest case of a broadcast AM radio (6A3, double sideband full carrier) signal operating with a carrier frequency f(c) of 600 kHz modulated at 100% with a 4.0 kHz sinusoid. We now have a signal that occupies the spectrum from 596 kHz to 604 kHz, and the Q of the output amp stage as well as the antenna must be low enough to not trim off the sidebands.

I am still confused. AS I know is the antenna size is directly related to wavelength so at higher frequencies we can have smaller antennas. The efficiency is directly related to size as it allows capturing more energy. If this is true then how does bandwith relate to antenna size?

@JWC Good point. I was considering only single element with length reduction below 1/2 (dipole) and 1/4 (ground plane) wavelength.
Next marketing breakthrough - a log periodic on a cellphone! (Just kidding)

"[Simply stated, these limitations are: "Bandwidth and antenna size are inversely related" and "efficiency and antenna size are
directly related." This means that in general, a larger antenna will have larger bandwidth and efficiency.]"
This is a bit confusing, if bandwidth is inversely related to antenna size, then a larger antenna would have a smaller bandwidth. The few times I made short antennas the bandwidth decreased as antenna length decreased. Am I missing something?
Otherwise a very interesting and well-written article.